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Suppose a baker claims that his bread height is more than 15 cm, on average. Several of his
customers do not believe him. To persuade his customers that he is right, the baker decides to
do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17
cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for
the height is 0.5 cm. and the distribution of heights is normal.
Question 3
An oil company claims that the sulfur content of its diesel fuel is at most 0.15. To check this
claim, the sulfur contents of 40 randomly chosen samples were determined; the resulting
sample mean, and sample standard deviation were .162 and .040. Using the 5 percent level of
significance, can we conclude that the company’s claims are invalid?
Question 4
A researcher claims that ANC Party will win in the next elections, especially in Gauteng
province. Statistical data reported that 23% voted for ANC Party in the last election. To test
the claim a researcher surveyed 80 people and found that 48 said they voted for ANC Party in
the last election. Is there enough evidence at α=0.05 to support this claim?

Respuesta :

Lanuel
  1. Since the p-value is approximately equal to zero (0), we can conclude that there is sufficient evidence that the true mean height for the baker's loaves of bread is greater than (>) 15 cm.
  2. Since 2.37 is greater than (>) 1.645, we reject the null hypothesis (H₀) at 5% level of significance. Therefore, we can conclude that the company’s claims are invalid.

What is a null hypothesis?

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

For the baker's claim, the appropriate null and alternative hypotheses would be given by:

H₀: μ ≤ 15

H₁: μ > 15

Since the standard deviation for the height is given, the population would have a normal distribution, and the population standard deviation is given by:

Population standard deviation = σ/√n

Population standard deviation = 0.5/√10

Population standard deviation = 0.16.

For the p-value, we have:

The p-value is the probability that a sample mean would be the same or greater than (≥) 17 cm. Thus, the p-value is given by:

p-value = P(x > 17) ≈ 0.

Since the p-value is approximately equal to zero (0), we can conclude that there is sufficient evidence that the true mean height for the baker's loaves of bread is greater than (>) 15 cm.

Question 3.

For the oil company's claim, the appropriate null and alternative hypotheses would be given by:

H₀: μ = 0.15

H₁: μ > 0.15

How to calculate value of the z-score?

The z-score can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }[/tex]

Where:

  • x is the sample mean.
  • u is the mean.
  • is the standard deviation.
  • n is the number of boys.

Substituting the given parameters into the formula, we have;

[tex]z=\frac{0.162\;-\;0.15}{\frac{0.04}{\sqrt{40} } }\\\\z=\frac{0.012}{\frac{0.4}{6.3246 } }[/tex]

z = 0.012/0.0633

z = 0.190.

From the z-table, a z-score of 0.190 is equal to a p-value of 2.37.

For the critical value, we have:

Critical probability (p*) = 1 - α/2

Critical probability (p*) = 1 - 0.1/2

Critical probability (p*) = 0.95.

Hence, the critical value is Zα/2 equal to 1.645.

Since 2.37 is greater than (>) 1.645, we reject the null hypothesis (H₀) at 5% level of significance. Therefore, we can conclude that the company’s claims are invalid.

Read more on null hypothesis here: https://brainly.com/question/14913351

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